How much money must be available if a person wants to withdraw $200 per month for five years at 6% annual interest compounded monthly
To determine how much money must be available if a person wants to withdraw $200 per month for five years at a 6% annual interest compounded monthly, we need to use the present value of an annuity formula.
The formula for calculating the present value of an annuity is:
PV = PMT * (1 - (1 + r/n)^(-nt)) / (r/n)
Where:
PV = Present Value
PMT = Payment per period
r = Annual interest rate (as a decimal)
n = Number of compounding periods per year
t = Number of years
In this case:
PMT = $200
r = 6% = 0.06 (as a decimal)
n = 12 (compounded monthly)
t = 5 years
Substituting the values into the formula:
PV = $200 * (1 - (1 + 0.06/12)^(-12*5)) / (0.06/12)
Simplifying the equation:
PV = $200 * (1 - (1.005)^(-60)) / (0.005)
Calculating the value inside the brackets:
PV = $200 * (1 - 0.598741) / 0.005
Calculating the final value:
PV ≈ $200 * 0.401259 / 0.005
PV ≈ $320.88 / 0.005
PV ≈ $64,176
Therefore, approximately $64,176 must be available in order to withdraw $200 per month for five years at 6% annual interest compounded monthly.